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—In this paper, we show how to compute an over-approximation for the reachable set of uncertain nonlinear continuous dynamical systems by using guaranteed set integration. We introduce two ways to do so. The first one is a full interval method which handles whole domains for set computation and relies on state-of-the-art validated numerical integration(More)
In this paper, we investigate nonlinear reachability computation in presence of model uncertainty, via guaranteed set integration. We show how this can be done by using the classical Müller's existence theorem. The core idea developed is to no longer deal with whole sets but to derive instead two nonlinear dynamical systems which involve no model(More)
This paper presents a contribution for restoring standing in paraplegia while using functional electrical stimulation (FES). Movement generation induced by FES remains mostly open looped and stimulus intensities are tuned empirically. To design an efficient closed-loop control, a preliminary study has been carried out to investigate the relationship between(More)
We address nonlinear reachability computation for uncertain monotone systems, those for which flows preserve a suitable partial orderings on initial conditions. In a previous work [1], we introduced a nonlinear hybridization approach to nonlinear continuous reachability computation. By analysing the signs of off-diagonal elements of system's Jacobian(More)
We investigate solution techniques for numerical constraint satisfaction problems and validated numerical set integration methods for computing reachable sets of nonlinear hybrid dynamical systems in presence of uncertainty. To use interval simulation tools with higher dimensional hybrid systems, while assuming large domains for either initial continuous(More)
This paper deals with set membership state estimation for continuous-time systems from discrete-time measurements, in the unknown but bounded error framework. The classical predictor-corrector approach to state estimation uses interval Taylor methods for solving the prediction phase, which are known to have poor performance in presence of large model or(More)
This paper introduces effective numerical methods for the planning and fast replanning of safe motions to ensure the safety, balance, and integrity of humanoid robots over the whole motion duration. Our safe methods do not depend on, nor are connected to, any type of modeling or constraints. To plan safe motions, certain constraints have to be satisfied(More)